Screw-type coolers for cooling hot particulate material, for example ashes from combustion plants with a cooled mantle and a cooled feed gear, are already known. For cooling of fine-grained ashes separated from flue gases in PFBC power plants, it has been found that prior art coolers of this kind do not provide satisfactory cooling. The material between two threads of the screw is transported axially in the cylinder without any mentionable mixing. A good contact and effective cooling between the powder mass is obtained only on the driving side of the screw. The screw cools the inner part of the powder mass only insignificantly. The cooling is ineffective. The material also has a tendency to form a layer with great heat transfer resistance on the inner side which makes up the major part of the cooling surface of the cooler. Only material that is brought into direct contact with the water-cooled rotor is effectively cooled. The cooling capacity is therefore reduced to such a considerable extent that satisfactory cooling in equipment with moderate dimensions is not obtained. A doubling or enlargement of a cooler entails increased space and higher construction costs.